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On the arithmetic of simple singularities of type E

Abstract:
An ADE Dynkin diagram gives rise to a family of algebraic curves. In this paper, we use arithmetic invariant theory to study the integral points of the curves associated to the exceptional diagrams E6,E7, E8. These curves are non-hyperelliptic of genus 3 or 4. We prove that a positive proportion of each family consists of curves with integral points everywhere locally but no integral points globally.
Publication status:
Published
Peer review status:
Peer reviewed

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Institution:
University of Oxford
Division:
College Only
Role:
Author
ORCID:
0000-0002-4480-636X
Publisher:
Springer
Journal:
Research in Number Theory More from this journal
Volume:
4
Issue:
2
Article number:
21
Publication date:
2018-04-16
Acceptance date:
2018-03-14
DOI:
EISSN:
2363-9555
ISSN:
2522-0160
Language:
English
Keywords:
Pubs id:
1136433
Local pid:
pubs:1136433
Deposit date:
2020-10-08

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